Shape control method and system for a rolling mill

ABSTRACT

A shape control system for a rolling mill comprises means for operating a roll positioning means to press down the rolls under a preselected load, when no strip to be rolled is fed between the rolls; a calculator of roll position variation for comparing the roll position under the preselected load with a preselected reference roll position; a calculator of roll crown variation for calculating the roll crown variation by using the output from said calculator of roll position variation and a preselected functional relationship; and a calculator of roll bending force for calculating the amount of a roll bending force to be corrected based on the output from said calculator of roll crown variation and feeding the thus calculated correction to roll bender control means.

BACKGROUND OF THE INVENTION

This invention relates to a method and system for controlling flatnessin sheet metal by detecting the variation in the roll crown.

Recently, there has arisen an increasingly demand for the accuracy inthe thickness of a cold rolled strip. With the development of anautomatic gauge control means (AGC), a satisfactory uniformity in gaugeof a strip can be attained in the rolling direction. However, nosatisfactory control method has been realized for achieving an accuracyin gauge of a strip in the widthwise direction and, especially, theflatness of the strip. A known method for controlling the flatness of astrip (or shape control) is a roll bending method, wherein the variationin the roll crown due to wear and/or thermal expansion (heat crown) ofrolls (the latter is caused by the heat radiation from the strip beingrolled as well as by the heat caused by the deformation of a strip) mustbe compensated for to control the flatness of a strip. This controlmethod, however, is no longer employed widely, because difficulties areencountered in determining the extent of the roll crown varied due towear and heat and therefore a roll bending force cannot be setbeforehand.

SUMMARY OF THE INVENTION

It is therefore a primary object of this invention to provide a methodfor controlling flatness of a strip in a rolling mill, by detecting theroll crown variation.

According to this method, the correlation between variations of the rollcrown and of the roll position under a preselected rolling load isdetermined beforehand; then the roll crown variation is measured duringoperation, as required; and the shape control means is controlleddepending on the thus measured roll position variation and thepredetermined correlation between variations of the roll crown and ofroll position.

In other words, the control method of this invention is based on thefinding that there is a linear proportional relation between the rollcrown variation ΔC_(R) during the repeated rolling operations and thevariation of roll position ΔS_(o) under a preselected rolling load.Based on said linear proportional relation, the roll crown variationΔC_(R) is determined indirectly from the variation of roll positionΔS_(o) for controlling the shape control means such as a roll bendingmeans.

The present invention provides suitable shape control systems forpracticing the aforesaid method.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a graph representing the relationship between the indicationvariation ΔS_(o) (or the variation of roll position under a preselectedrolling load) at the time when the roll gap equals to zero and the rollcrown variation ΔC_(R) ;

FIG. 2 is a block diagram of the shape control system for a rolling millaccording to one embodiment of this invention; and

FIG. 3 is a block diagram of the shape control system for a rolling millaccording to another embodiment of this invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Before describing preferred embodiments, the theoretical explanation forthe control method according to this invention will first be set forthhereinunder.

Generally, when rolling a strip, an irregular thickness distributiontakes place widthwise of the strip, with there resulting a strip crown.Such a strip crown C_(S) is expressed by the following relation:

    C.sub.S = C.sub.R + C.sub.1 (1)

where, C_(R) is a roll crown and C₁ is a crown formed in a rolled stripdue to the causes other than the roll crown. The crown C₁ includes acrown C₂ intentionally formed in the strip by means of a roll bender anda crown C₃ caused in the strip under a rolling load.

    C.sub.1 = C.sub.2 + C.sub.3 (2)

These crowns C₂ and C₃ are discussed, for example, in the "Iron andSteel Engineer" Vol. 42, No. 8, 1965, p. 73 -83 by Stone. According toStone's discussion, when a back roll bending is applied, the crown C₂will be expressed as, ##EQU1## where, F is a roll bending force; a is amoment arm of the bending force; W is the strip width; E is the Young'smodulus of the roll and I is the moment of inertia of the backup roll.If 4E/aW² is substituted by K₁, then the Equation (3) will be simplifiedas follows: ##EQU2## This relation is maintained also in case of a workroll bending, although K₁ has a different value.

According to Stone's discussion, C₃ is expressed as ##EQU3## where, P isa rolling load; h is a distance from the side edge of the strip to thecenter of the backup roll bearing; and D is a diameter of the backuproll.

It will be appreciated that Equation (1) can be rewritten as follows:##EQU4## Also Equation (6) will be rewritten as follows: ##EQU5## whereΔ means mathematical symbol of variation. To obtain a flat rolled strip,ΔC_(S) must be zero. Therefore,

    ΔF = K.sub.1 (ΔC.sub.R +ΔC.sub.3) (8)

If roll bending force which offsets roll crown variation ΔC_(R) isdenoted by ΔF_(R), ΔF_(R) is expressed as follows:

    ΔF.sub.R = K.sub.1 ΔC.sub.R (9)

The study made by the inventors reveals that variation ΔS_(o) inindicated value of roll position under a preselected rolling load at thetime when the roll gap equals to zero is directly proportional to theroll crown variation ΔC_(R) as shown in FIG. 1.

    ΔC.sub.R = K.sub.2 ΔS.sub.o (10) where K.sub.2 is a constant value represented by the slope of the line in FIG. 1. From Equations (9) and (10),

    ΔF.sub.R = KΔS.sub.o (11)

where, K = K₁.sup.. K.sub. 2. Equation (11) means that the roll bendingforce which offsets the roll crown variation is directly proportional tothe variation ΔS_(o), and therefore a roll bending force offsetting theroll crown variation can be determined by detecting the variation ΔS_(o)in indicated value.

Illustrated in FIG. 2 is a schematic view illustrating the arrangementof the shape control system according to one embodiment of the presentinvention, the system detecting a roll crown variation and controlling,in accordance with the foregoing principle, the shape of the strip beingrolled. Indicated at 1, 2 and 3 are a steel strip being rolled, workrolls and backup rolls, respectively. Between the roll neck of the lowerbackup roll 3 and roll positioning means 4 are interposed a rollposition detector 5 and a load detector 6, which are respectivelyconnected to a calculator of roll position variation 8 and to a rollingload comparator 9 included in a roll crown variation detector 7 forfeeding inputs into the detector 7 which forms the essential part of thepresent inventon.

The roll crown variation detector 7 comprises reference load settingmeans 10, load comparator 9, reference roll position setting means 11,calculator of roll position variation 8, calculator of roll crownvariation 12, relay R₁ for applying the output signal from said loadcomparator 9 into the roll positioning means 4, and relay R₂ foroperating indicator of the roll position detector 5. The relays R₁ andR₂ are so arranged that they are closed upon receiving sequence signalsfrom an external sequence control means 13 (for example, a computer).

Now the operation of the roll crown variation detector 7 having theforegoing construction will be described in connection with a coldrolling mill. After a predetermined number of coils have been rolled, aninstruction signal for detecting the roll crown variation is producedfrom the sequence control means 13 to be fed to the roll crown variationdetector 7. As a result, the relay R₁ (which is arranged on the outputline from the load comparator 9 adapted to compare the reference loadsignal P_(F) from the reference load setting means 10 with the outputsignal P from the load detector 6) is closed to thereby feed the outputfrom the load comparator 9 to the roll positioning means 4. Then, theroll positioning means 4 starts operating and continues to work until acondition of P = P_(F) is reached. Simultaneous therewith, the rollpositioning means 4 stops operating, the roll position detector 5 startsoperating to feed the roll position S_(o) under a load P_(F) to thecalculator of roll position variation 8. The calculator 8 thencalculates a difference ΔS.sub. o between the input signal S_(oF) fromthe reference roll position setting means 11 and the input signal S_(o)from the roll position detector 5 for feeding the difference ΔS_(o) tothe calculator of roll crown variation 12. By use of this input ΔS_(o),the calculator of roll crown variation 12 calculates the above-mentionedrelation ΔC_(R) = K₂ ΔS_(o) and produces an output ΔC_(R). Relay R₂ isclosed by an instruction signal of the sequence control means 13 forchanging S_(o) to S_(oF) if necessary.

With the foregoing arrangement, the roll crown variation can be detectedautomatically without dismounting a roll from the rolling mill. Thedetected roll crown variation is then fed to a shape control means aswill be described later, for thereby effecting the calculation for shapecontrol, that is, a calculation for determining the optimum rollbending. The shape control means of the present invention includes rollcrown variation detector 7, the calculator of optimum roll bending force15 operative in response to the output from said detector 7, and rollbender control means 16 operative in response to the output from saidcalculator 15 to control a roll bender 17. The calculator of optimumroll bending force 15 calculates the optimum roll bending force F. FromEquation (6), force F will be expressed as follows:

    F = K.sub.1 (C.sub.R + C.sub.3 - C.sub.S) (12)

This is a formula for obtaining the optimum roll bending force F toproduce a strip having a predetermined crown C_(S).

By introducing the roll crown value C_(R) obtained after the precedingrolling operation, Equation (12) will be changed as follows:

    F = K.sub.1 (C.sub.R + ΔC.sub.R + C.sub.3 - C.sub.S) (13)

It will be understood from this Formula (13) that the optimum rollbending force F can be obtained only by detecting the roll crownvariation ΔC_(R).

As has been described hereinabove, this invention permits a shapecontrol calculation by detecting the roll crown variation, which has notbeen detectable heretofore. The shape control calculation makes possibleto effect a roll bender control by use of a computer, thereby greatlycontributing to improve the quality of a strip by eliminating a dangerthat the strip of inferior shape is produced.

Although the invention has been described hereinabove with reference toan embodiment wherein the roll crown variation is measured depending onthe detected roll position variation at the zero adjustment which iseffected before rolling, it is also possible to correct the roll crownvariation during rolling by use of an automatic gauge control system(AGC) as in the second embodiment of FIG. 3. According to this secondembodiment the rolling mill is provided with work rolls 22 and backuprolls 23 for rolling a strip 21. The rolling load P_(F), roll positionS_(F), bending force F_(F) and a gauge h_(F) of a strip are set byreference value setting means 28, 29, 30 and 31, respectively. Thedetected load P from a rolling load detector 24 and the referencerolling load P_(F) from the reference rolling load setting means 28 arefed to a comparator 32 to determine their difference ΔP, which is thenfed to calculator 37. The detected roll position S from a roll positiondetector 25 and the reference roll position S_(F) from the referenceroll position setting means 29 are fed to a comparator 33 to determinetheir difference ΔS, which is then fed to the calculator 37. Similarly,the detected strip gauge h from a strip gauge detector 27 and thereference strip gauge h_(F) from the reference strip gauge setting means31 are fed to a comparator 36 to determine their difference Δh, which isthen fed to the calculator 37. By use of these inputs ΔP, ΔS and Δh, thecalculator 37 performs a calculation in accordance with the followingautomatic gauge control formula to thereby feed a value ΔS_(o) tocalculator 38. ##EQU6## where, Km is a mill modulus. ΔS_(o) correspondsto variation of roll position at the time when roll gap and rolling loadequal to zero. In accordance with formula (11), the calculator 38calculates ΔF_(R) and feeds the same to a calculator 34. The calculator34 adds the output F_(F) from the reference roll bending force settingmeans 30 to the calculated ΔF_(R) to obtain a sum F_(C) and then feedsthe sum F_(C) to a comparator 35, which in turn calculates thedifference ΔF between said sum F_(C) and the output F from the rollbending force detector 26, for thereby operating a roll bending forcecontrol means 39 in response to the calculated difference ΔF. It will beappreciated that, with this embodiment, the variation in the rollbending force with respect to the variation in the roll crown, of whichautomatic control has been unattainable heretofore, can be correctedcontinuously.

What is claimed is:
 1. A shape control system for use with a rollingmill, the system comprising means for detecting the rolling load androll position, means for determining the variation roll position ΔS_(o)from the detected rolling load and roll position; means for calculatingthe roll crown variation ΔC_(R) from said variation ΔS_(o) in accordancewith a preselected functional relation; and means for controlling theroll bending means in response to the output from means for saidcalculator.
 2. A shape control system for use with a rolling mill, thesystem comprising means for operating roll positioning means to pressdown the rolls under a predetermined load when the roll gap equals tozero; a calculator means of roll position variation for comparing theposition of the rolls at the time when the rolls are pressed down undersaid predetermined load with a preselected reference roll position forproviding a roll position variation signal; a calculator means of rollcrown variation for calculating the roll crown variation from said rollposition variation signal in accordance with a preselected functionalrelation; and calculator means of roll bending force for calculating theamount of the roll bending force correction from the output from saidcalculator means of roll crown variation and feeding the amount of theroll bending force corrected to a roll bender control means.
 3. A shapecontrol system for use with a rolling mill, the system comprising firstmeans for detecting the rolling load; second means for detecting a rollposition during rolling; third means for detecting the strip gauge onthe outlet side; fourth means for detecting the roll bending force ofthe roll bender; calculator means for calculating the amount of the rollbending force which would correct for the roll crown variationcalculated from the values detected by said first, second, third andfourth means in accordance with a preselected functional relation; andmeans for correcting the roll bending force depending on the valuecalculated by said calculator means.
 4. A shape control system accordingto claim 1, wherein the means for calculating calculates ΔC_(R) inaccordance with the functional relation ΔC_(R) = K₂ ΔS_(o) where K₂ is aconstant.
 5. A shape control method for use in a rolling mill comprisingthe steps of determining a variation of roll position ΔS_(o)corresponding to a time when the roll gap is zero and under preselectedrolling load, and converting the variation ΔS_(o) into a roll crownvariation ΔC_(R) in accordance with a predetermined functional relationfor thereby controlling a shape control means in dependence on the rollcrown variation ΔC_(R).
 6. A shape control method for use in a rollingmill according to claim 5, further comprising the step of controllingthe shape control means in dependence on the roll crown variationΔC_(R).
 7. A shape control method for use in a rolling mill according toclaim 5, wherein the predetermined functional relation is ΔC_(R) = K₂ΔS_(o) wherein K₂ is a constant.
 8. A shape control method for use in arolling mill according to claim 5, wherein the step of determining avariation of roll position ΔS_(o) includes measuring the roll positionunder a preselected rolling load with the roll gap set to zero andcomparing the measured roll position with a preselected reference rollposition to determine the variation of roll position ΔS_(o).
 9. A shapecontrol method for use in a rolling mill according to claim 5, whereinthe step of determining a variation of roll position ΔS_(o) includesmeasuring the roll position, rolling load and strip gauge, comparing themeasured roll position, rolling load and strip gauge with correspondingpreset reference values to determine the variation from the presetreference values, and obtaining the variation ΔS_(o) from thevariations.
 10. A shape control method for use in a rolling millaccording to claim 9, wherein the variation in roll position is ΔS, thevariation in rolling load is ΔP, and the variation in strip gauge is Δh,and the variation ΔSo is obtained in accordance with ΔS_(o) =ΔS -Δh +ΔP/Km where Km is a mill modulus.
 11. A shape control method for use ina rolling mill according to claim 5, wherein a roll bending means isused as the shape control means, and further comprising the step ofcorrecting the optimum roll bending force of the roll bending means inresponse to the variation ΔS_(o).